idiosyncratic perspectives on philosophy of science, its history, and related issues in logic

6/22/2017

Tarski, Carnap, and semantics

Two things:

1. Synthese recently published Pierre Wagner's article Carnapian and Tarskian Semantics, which outlines some important differences between semantics as Tarski conceived it (at least in the 1930s-40s) and as Carnap conceived it. This is important for anyone who cares about the development of semantics in logic; I'd been hoping someone would write this paper, because (a) I thought it should be written, but (b) I didn't really want to do it myself. Wagner's piece is really valuable, in my opinion. And not merely for antiquarian reasons: many today have the feeling that semantics in logic (roughly: model theory) is the natural/ inevitable way to come at semantics in logic. But how exactly to pursue semantics was actually very much up for debate and in flux for about 20 years after Tarski's 1933 "On the Concept of Truth in Formalized Languages." And the semantics in that monograph is NOT what you would find in a logic textbook today.

2. I am currently putting the finishing touches on volume 7 of the Collected Works of Rudolf Carnap, which is composed of Carnap's three books on semantics (Introduction to Semantics, Formalization of Logic, and Meaning and Necessity). There is a remark in Intro to Semantics that is relevant to Wagner's topic, which Wagner cited (p.104), but I think might be worth trying to investigate in more detail. Carnap writes:
our [= Tarski's and my] conceptions of semantics seem to diverge at certain points. First ... I emphasize the distinction between semantics and syntax, i.e. between semantical systems as interpreted language systems and purely formal, uninterpreted calculi, while for Tarski there seems to be no sharp demarcation. (1942, pp. vi-vii)

I have two thoughts about this quotation: (i) Is Carnap right? Or did he misunderstand Tarski? (Carnap had had LOTS of private conversations with Tarski by this point, so the prior probability I assign to me understanding Tarski better than Carnap does is pretty low.) (ii) If Carnap is right about Tarski on this point, then (in my opinion) we today should give much more credit to Carnap for our current way of doing semantics in logic than most folks currently do. We often talk about 'Tarskian semantics' today as a short-hand label for what we are doing, but if there were 'no sharp demarcation' between model theory and proof theory (i.e. between semantics and syntax), then the discipline of logic would look very different today.

1 Comments:

Any clue when some of the volumes in the collected works are actually going to come out? The most recent thing I could find on the web page was a posting from last year claiming some volumes would be available before the end of the year, which seems not to have worked out.